provides updating and downdating for rank deficient linear
least squares solutions, complete orthogonal factorization,
and Moore-Penrose inverses
- CALL LUPDT( lup, bup, sup, l, z<, b,
The LUPDT subroutine returns the following values:
- is an n ×n lower triangular matrix L that
is updated or downdated by using the q rows in Z.
- is an n ×p matrix B of right-hand sides that
is updated or downdated by using the q rows in Y.
If b is not specified, bup is not accessible.
- is a p vector of square roots of residual sum of squares
that is updated or downdated by using the q rows in Y.
If ssq is not specified, sup is not accessible.
The inputs to the LUPDT subroutine are as follows:
- specifies an n ×n lower triangular matrix
L to be updated or downdated by q row vectors
z stored in the q ×n matrix Z.
Only the lower triangle of l is used; the
upper triangle may contain any information.
- is a q ×n matrix Z used rowwise
to update or downdate the matrix L.
- specifies an optional n ×p matrix
B of right-hand sides that have to be
updated or downdated simultaneously with L.
If b is specified, the argument y must be specified.
- specifies an optional q ×p matrix Y used rowwise
to update or downdate the right-hand-side matrix B.
- specifies an optional p ×1 vector that,
if b is specified, specifies the square root of
the error sum of squares that should be updated
or downdated simultaneously with L and b.
The relevant formula for the LUPDT call is
.See the LUPDT Example section
for an example of the LUPDT call.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.